ATL-PHYS-PUB-2010-014 28 October 2010 ATLAS NOTE October 28, 2010 First tuning of HERWIG/J IMMY to ATLAS data The ATLAS Collaboration Abstract This note describes the first systematic tuning of the HERWIG generator to ATLAS data, with the J IMMY model for multiple parton interactions. We present a new set of HERWIG/J IMMY tunes for the MRST LO*, CTEQ6L1 and CTEQ6.6 PDFs, collectively titled “AUET1” (”ATLAS Underlying Event Tune 1”). The MC09 HERWIG/J IMMY tuning was taken as a starting point for the AUET1 tunes, but important methodological modifications have been made, in particular use of more tuning parameters. In the tuning of the regularisation scale for multiple scattering, an energy- dependence ansatz similar to the one found in the PYTHIA 6 generator has been used. While CDF strongly biased towards ATLAS underlying event data, particularly at 7 TeV.
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ATLAS NOTE
October 28, 2010
First tuning of HERWIG/JIMMY to ATLAS data
The ATLAS Collaboration
Abstract
This note describes the first systematic tuning of the HERWIG generator to ATLAS data, withthe JIMMY model for multiple parton interactions. We present a new set of HERWIG/JIMMY
tunes for the MRST LO∗, CTEQ6L1 and CTEQ6.6 PDFs, collectively titled “AUET1” (”ATLASUnderlying Event Tune 1”). The MC09 HERWIG/JIMMY tuning was taken as a starting point forthe AUET1 tunes, but important methodological modifications have been made, in particular use ofmore tuning parameters. In the tuning of the regularisation scale for multiple scattering, an energy-dependence ansatz similar to the one found in the PYTHIA 6 generator has been used. While CDFstrongly biased towards ATLAS underlying event data, particularly at 7 TeV.
1 Introduction
MC event generators are a crucial tool for experimental particle physics, providing not just flexible and highly-differential implementations of physics models against which we can test our results, but also a source ofsimulated events for analysis design and detector-effect unfolding. While the first of these three issues islargely a matter for the theorists, a good match between simulation and data is necessary for the other two.Event generators are at their least predictive when dealing with soft, non-perturbative QCD effects, wheretheir modelling is guided by asymptotic behaviours and extrapolation to more typical conditions introducesparameters whose values can be determined only by comparison to data. This process of parameter optimisationis known as “tuning”. Different event generators favour different philosophies of what may be tuned, butthe most obvious and uncontroversial areas are the soft QCD processes of hadronisation and beam-particleremnant/bulk effects, the latter typically modelled with some variant of multiple parton interactions (MPI). Ofthese, hadronisation is most cleanly tuned to event shape and identified particle data from e+e− colliders, whileMPI is a hadron collider effect whose effects are most obviously seen in minimum bias (MB) and underlyingevent (UE) observables1). In this note, as in previous ATLAS tuning studies, we focus on the tuning of MPIparameters.
The MC09 tune [1] of the PYTHIA6 generator [2], based on Tevatron MB and UE data available before the startof LHC data running, provides an excellent description of those data, but was seen to significantly underestimatelevels of MPI activity in ATLAS MB and UE data. The ATLAS AMBT1 tune [3] was created as a responseto this deficiency, producing a much-improved description of ATLAS data for use in the MC10 simulationproduction. An exactly analogous situation exists for the MC09 tunes of the Fortran HERWIG generator [4] andits JIMMY add-on [5, 6], which provides an MPI model similar to that in PYTHIA 6 but is unable to describeminimum bias physics. Constructing updated HERWIG/JIMMY tunes which can describe the first ATLASunderlying event data, also for use in the MC10 production, is the subject of this note.
Since the MC09 tuning of HERWIG/JIMMY, ATLAS MC tuning has almost ubiquitously made use of statisticaltools to optimise the MC fit to the reference data. By comparison, in the MC09 tuning round this approachwas only taken for the CTEQ6.6 PDF [7] tune of HERWIG/JIMMY and the MC09c PYTHIA 6 tune. The MC09HERWIG/JIMMY tuning also retained the MC08 ansatz for MPI energy extrapolation and did not vary anynon-MPI parameters, i.e. the initial state parton shower, intrinsic pT, etc. were left at default values. Thetuning described here improves on the MC08 and MC09 methodologies by including all these aspects in thetuning process, as well as the ATLAS UE data. This new set of tunes is titled “AUET1”, in analogy with theATLAS PYTHIA 6 AMBT1 tune, and consists of equivalent tunes for the MRST LO∗ MC-modified leadingorder PDF [8], the leading order (LO) CTEQ6L1 PDF [9], and the next-to-leading order (NLO) CTEQ6.6PDF [7].
2 Tuning setup
For this, as in other ATLAS MC tuning studies, we do not use the ATLAS interface to the generator: it isadequate and easier to scan the tuning parameter space with the standalone generator, in this case via theAGILe generator interface [10]. The Rivet system [11] was used to analyse the generated events, and the
1)The distinction is that MB is dominated by purely soft QCD scattering with minimal event selection criteria, whereas UE is thesoft QCD component which forms an irreducible background in events with an identified hard scattering, e.g. a dijet or Drell-Yan eventselection.
2
Professor system was applied to produce the tuned parameters by a combination of response parameterisationand numerical fit optimisation [12].
The generator setup is in most aspects the same as for MC09: we describe only the differences. One differencein the underlying generator model for this collection of tunes is found in the setup of the space-like initial-stateshower. As opposed to previous ATLAS use of HERWIG, we decided to use a more sophisticated modellingof the ISR shower in the HERWIG model by setting ISPAC = 2, as this is recommended by the authors. Thissetting allows for emissions below the ISR shower IR cut-off parameter, QSPAC, giving a smoother matchingto the PDF. By comparison, the MC08 and MC09 setups used the default ISPAC = 0 setting, which applies asharp IR cutoff in the space-like shower. We attempted to include QSPAC itself in a first round of tunes, but withvariations between 0.5 and 5 GeV did not find any of the available CDF or ATLAS observables to be sensitiveto its value. We hence kept QSPAC at its MC09/default value of 2.5 GeV.
We note that ATLAS has yet to tune generator final state showers, including that of HERWIG, to best describeevent shapes from LEP and other e+ e− colliders. This deficiency is not resolved for HERWIG by this note: itwill be addressed along with the other generators when a more complete shower tuning round is completed,including ATLAS jet data.
Since the JIMMY MPI model is by design not valid for multiple scattering where the signal process is itself asoft scatter, minimum bias data cannot be used for tuning of this generator. As the underlying event data fromATLAS and CDF represent a smooth transition from minimum bias to UE-type processes, the softest parts ofthese observables must also be excluded from fits. In the ATLAS UE data, and that from the CDF 2001 UEstudy, there is not a very strong distinction between primary and secondary scatters, and so JIMMY is instructedto generate the softest possible scatters by setting its UE mode to 0, via the JMUEO = 0 parameter setting (seeref. [6]).
2.1 Tuning parameters
The cut-off for multiple parton interactions modelled with JIMMY is a single parameter, PTJIM, without anydependence on the hadronic centre-of-mass energy,
√s. In order to make the model fit to data for various
collider energies we apply the following energy dependence of PTJIM which is inspired by the “pomeron-inspired” energy evolution of the similar cut-off in the PYTHIA6 model:
PTJIM(√
s) = PTJIM0 ·( √
s1800 GeV
)EXP
, (1)
where the tuning parameter PTJIM0 is the value for PTJIM (√
s) at the reference energy 1800 GeV and the EXPparameter controls the rate of energy evolution. The EXP parameter was manually set at 0.274 in the MC08JIMMY tune, and was kept fixed at this value in the MC09 JIMMY tunes (for all PDFs). The final MPI parameterfor tuning is the hadronic form factor radius: although JIMMY allows to set the proton and antiproton radiusseparately (JMRAD(73), JMRAD(93)), we use the same variable, PRRAD, for both.
It was noticed during the initial exploratory tunes that since the MC08 and MC09 tunes only varied MPIparameters, HERWIG was being run without any intrinsic pT smearing. This parameter typically adds an extra1 or 2 GeV to pT measurements and is important for the description of the low-pT part of e.g. the Z bosonpT spectrum: the intrinsic pT Gaussian smearing is needed to move an anomalous peak at zero into the peakof the distribution, and in determining the line-shape and peak position. The default setting of the intrinsic pTGaussian width variable, PTRMS = 0, is strongly disfavoured. Since, of our tuning observables, only the CDF
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Figure 1: (a) CDF Z pT peak with different HERWIG intrinsic pTs from 0 to 1.5 GeV. The problem with thePTRMS= 0 setting of previous tunes may be seen from the behaviour of that curve in the first (zero-pT) bin. ForkT = 0.5 GeV this overshoot has been smeared into the pre-peak bins, giving them an excess. More acceptablevalues lie in the region from 1 GeV to 1.5 GeV, of which we chose 1.2 GeV. (b) Comparison of tunes: AUET1= ATLAS Underlying Event Tune 1 (LO∗) with PTRMS= 1.2 vs. ATLAS MC09 with PTRMS= 0.
Z pT measurement gives a strong and unambiguous handle on value of PTRMS, we decided to manually tunethis as an isolated single variable with a single observable, rather than add an extra parameter to the multi-dimensional part of the tuning. Comparing the Z pT line-shapes [13] with PTRMS values between 0.5 and 2.0,as seen in Figure 1, we chose a value of PTRMS = 1.2 (GeV) as giving the best results and used this as a basisfor the rest of the tuning. This choice was virtually insensitive to the choice of PDF.
After fixing QSPAC to its default value, and after tuning PTRMS manually, the remaining step was a three-dimensional tuning of PTJIM0, EXP, and PRRAD using the Professor tool according to the procedure described inthe AMBT1 [3] and Professor [12] papers. The relevant fixed settings and sampling ranges for these parameters,and those for the MC09 tune, are shown in Table 1. The ranges were determined as suitable for all three PDFs bymeans of observable envelope plots, which showed complete coverage of the observables valid for the JIMMY
model by the sampled parameter points.
3 Tuning and results
Several iterations of the tuning observable weights were explored before converging on a balance well-matchedto current ATLAS use. As the JIMMY MPI model is fundamentally not able to describe minimum bias data,MB observables were entirely excluded from the fit. Of the remaining UE data, weightings were applied tothe observables as described in ref. [12]. The weights were chosen to strongly bias the fit towards the ATLAS7 TeV data (since that is the relevant data to which the MC10 samples will be compared), then to the ATLAS900 GeV data, and finally to CDF UE data. The purpose of the CDF data is to protect the tune against over-fitting to the ATLAS track-based UE measurements. The observables used are a subset of those used in thePYTHIA AMBT1 tune, and are described in detail in ref. [3] – while the PYTHIA tune could use both MB and
Tuned JIMMY parametersPRRAD (Anti)proton radius (GeV2) 2.2 1.5 2.5 1.69 1.90 1.82PTJIM (7) MPI cut-off at 7 TeV (GeV) 5.22 4.14 3.86 3.13PTJIM (10) MPI cut-off at 10 TeV (GeV) 5.76 4.56 4.26 3.38PTJIM (14) MPI cut-off at 14 TeV (GeV) 6.32 5.00 4.68 3.64
Table 1: Final tuned parameter values for the AUET1 tunes of HERWIG/JIMMY, compared to those for theATLAS MC09 (LO∗) tune. The imin/max identify the sampling boundaries in the tuning procedure.
UE data, only the UE data (from CDF at Tevatron Runs I & II, and from the first ATLAS studies) can be usedto tune JIMMY. The fit weights and ranges of application for these tunes are tabulated in Table 2.
Recent forms of the PYTHIA MPI model contain a “colour-reconnection” model, i.e. an attempt to dynamicallyreconfigure colour string topologies to more energetically favourable configurations. This mechanism reducesthe average length of colour strings, and hence the number of radiated hadrons, giving a higher average pT perparticle. Data from the Tevatron has indicated that something like a colour reconnection model is needed inPYTHIA 6 to describe the 〈pT〉 vs. Nch observable in minimum bias events, and in recent tuning efforts it wasalso found to be important: the PYTHIA MC09c tune was explicitly created to vary the reconnection strength inPYTHIA MC09 to better describe minimum bias data, and it was again found to be important in the constructionof the PYTHIA AMBT1 tune.
The JIMMY MPI model notably contains no such colour-reconnection model, at least in part because its hadro-nisation model is not based on the colour string concept. In the Herwig++ generator there has been recent andapparently successful work on implementing colour reconfiguration at the hadronisation level, but again JIMMY
contains no such mechanism. We therefore expect that the JIMMY model may have difficulty describing thebalance of pT and particle number flow in soft scattering processes, and so it proves: JIMMY was found to beunable to describe the 〈pT〉 vs. Nch data (see Figure 6) in this tune at the same time as the UE profiles, whereasthe MC09 tune (without the ATLAS profile constraints) fits 〈pT〉 vs. Nch fairly well. As this tuning difficultyis directly associated with a known model shortcoming, a choice had to be made between which of the ∑ pTor Nch UE profile plots (in Figures 4 and 5) should be better-described. It was not possible to achieve a gooddescription of both at the same time. Since most ATLAS analysis quantities for which a good MPI descriptionis required are constructed from pT and energy flows rather than raw track numbers, we chose to place higherweight on the ∑ pT observables.
The fit was further finessed by awareness of public, but yet-unfinalised ATLAS UE data at 7 TeV with much-increased statistics in the UE “plateau” region, compared to the first round of UE results used in our fit. Thehigher-statistics data shows that the plateau actually has slightly higher plateau region activity than indicated
5
Observable√
s Fit range Weight
ATLAS track-based underlying event [14]Toward region Nchg density vs. pT (leading track) 7 TeV > 4.0 GeV 5.0Transverse region Nchg density vs. pT (leading track) 7 TeV > 4.0 GeV 10.0Away region Nchg density vs. pT (leading track) 7 TeV > 4.0 GeV 5.0Toward region ∑ pT density vs. pT (leading track) 7 TeV > 4.0 GeV 10.0Transverse region ∑ pT density vs. pT (leading track) 7 TeV 4.0 – 8.0 GeV 80.0
> 8.0 GeV 20.0Away region ∑ pT density vs. pT (leading track) 7 TeV > 4.0 GeV 10.0
Toward region Nchg density vs. pT (leading track) 900 GeV > 3.0 GeV 2.0Transverse region Nchg density vs. pT (leading track) 900 GeV > 3.0 GeV 5.0Away region Nchg density vs. pT (leading track) 900 GeV > 3.0 GeV 2.0Toward region ∑ pT density vs. pT (leading track) 900 GeV > 2.5 GeV 5.0Transverse region ∑ pT density vs. pT (leading track) 900 GeV 2.5 – 5.0 GeV 40.0
> 5.0 GeV 10.0Away region ∑ pT density vs. pT (leading track) 900 GeV > 2.5 GeV 5.0
CDF Run I underlying event analysis [15]Nch (toward) for min-bias 1800 GeV > 4.0 GeV 0.5Nch (transverse) for min-bias 1800 GeV > 4.0 GeV 0.5Nch (away) for min-bias 1800 GeV > 4.0 GeV 0.5Nch (toward) for JET20 1800 GeV 0.5Nch (transverse) for JET20 1800 GeV 0.5Nch (away) for JET20 1800 GeV 0.5psum
T (toward) for min-bias 1800 GeV > 4.0 GeV 1.0psum
T (transverse) for min-bias 1800 GeV > 4.0 GeV 1.0psum
T (away) for min-bias 1800 GeV > 4.0 GeV 1.0psum
T (toward) for JET20 1800 GeV 2.0psum
T (transverse) for JET20 1800 GeV 2.0psum
T (away) for JET20 1800 GeV 2.0pT distribution (transverse, plead
T > 2 GeV 1800 GeV 1.0pT distribution (transverse, plead
T > 5 GeV 1800 GeV 1.0pT distribution (transverse, plead
T > 30 GeV 1800 GeV 1.0
CDF Run I transverse cone and ‘Swiss cheese’ UE studies [16]〈pmax
T 〉 vs. E leadT 1800 GeV 1.0
〈pminT 〉 vs. E lead
T 1800 GeV 1.0Nmax vs. E lead
T 1800 GeV 0.5Nmin vs. E lead
T 1800 GeV 0.5Swiss Cheese psum
T vs. E leadT (for removal of 2 jets) 1800 GeV 5.0
Swiss Cheese psumT vs. E lead
T (for removal of 3 jets) 1800 GeV 5.0〈pmax
T 〉 vs. E leadT 630 GeV 1.0
〈pminT 〉 vs. E lead
T 630 GeV 1.0〈pdiff
T 〉 vs. E leadT 630 GeV 1.0
Swiss Cheese psumT vs. E lead
T (for removal of 2 jets) 630 GeV 5.0Swiss Cheese psum
T vs. E leadT (for removal of 3 jets) 630 GeV 5.0
Table 2: Observable–weight combinations used for the final tunes. Where the fit has been made to a restrictedrange in leading pT or ET, the fit range for that weight is shown in the “Fit range” column.6
Figure 2: The spread of tuning results for the PTJIM0 and EXP parameter tunes, using cubic generator responseparameterisations with all generator runs (red circles) and with subsets of generator runs (black crosses). Fig-ures (a), (c) & (e) show the results for PTJIM0; Figures (b), (d) & (f) show the results for EXP.
(f) Correlation between tune results for individual tuneparameters (CTEQ6.6)
Figure 3: The spread of tuning results for the PRRAD parameter tuning, using cubic generator response param-eterisations with all generator runs (red circles) and with subsets of generator runs (black crosses) is shown inFigures (a), (c) & (e). Figures (b), (d) & (f), show the correlation coefficients between the optimised parameters,as calculated from the covariance matrix of the sample of minimisation results.8
by the central values of the lower-statistics data used here for tuning. We took advantage of this qualitativeknowledge to increase the weighting at the tops of the ATLAS UE transverse profile ramps (the middle rowsin Figures 4 and 5) where the MC undershoots. This results in a slight MC overshoot of the ∑ pT plateau data,slightly improving the quality of the fit to the data region with the smallest statistical errors, and also bringingthe plateau fit slightly closer to the full-statistics data than a naıve treatment with uniform weightings wouldhave obtained. These extra weightings on the tops of the UE ramps, where the JIMMY model is valid andATLAS has high-statistics data, are again documented in Table 2.
The resulting tunes, which we collectively title “JIMMY AUET1” (for “ATLAS UE tune #1” in keeping withthe nomenclature used for the ATLAS PYTHIA6 AMBT1 tune) give a greatly improved description of ATLASsoft QCD data compared to the MC09 tune. The AUET1 tune parameters are shown in Table 1. We note thatthis improvement has been made at the slight cost of fit quality in the UE data from CDF gathered using theRun I minimum bias trigger. Given the basic nature of the energy evolution ansatz, the lack of parameterisationhandles compared to PYTHIA 6, and the relative importance of ATLAS and CDF fit quality from the point ofview of ATLAS simulation production, we consider this to be an acceptable compromise.
Figures 2 to 3 show the spread of tuning results for each parameter against the Professor heuristic χ2, for eachPDF. Each point is from a separate tune, made using various combinations of generator runs at points in theparameter space. The horizontal spread of points indicates the degree of uncertainty in the tune procedure,by using only a subset of 30 out of 39 available points from which to build each tune (or 31 out of 38 forCTEQ6.6). A narrow spread shows well-constrained parameters with little sensitivity to the input MC runs,and hence we see that all three parameters are well-determined, the largest spread being seen for PRRAD in thenon-LO∗ PDF tunes. The red points are the unique tunes using all available input runs. These are the finalAUET1 tune points, and the fact that they lie safely within the spread of run-subset tunes indicates that biasfrom the parameter sampling is not an issue. Figure 3 also shows the correlation of parameters: EXP is seen tobe relatively independent of the other two parameters, especially for the LO∗ PDF, while PTJIM0 and PRRAD
are positively correlated. This is expected, since PTJIM0 and PRRAD have competing effects and hence theirtuned values must be positively correlated to maintain quality of fit, as has been seen before in the tuning ofsimilar models [17].
In the CTEQ6.6 tune results, the very different value of EXP is an interesting development which we believeindicates that the JIMMY model and our evolution ansatz are being strained by the data. We have no robustunderstanding of what drove this strong difference, or whether it is connected to the significant correlationbetween the cutoff evolution exponent and the hadronic radius parameter: a similar correlation also exists forthe CTEQ6L1 tune, which has a similar EXP value to the LO∗ tune. A similar study of equivalent tuning ofPYTHIA 6 to three PDFs with the Professor tool resulted in tunes with very stable cutoff exponents, but thatmodel could trade off colour-reconnection and multiple matter distribution parameters (cf. PRRAD) to obtainthe best fit. A reassuring physical feature of the AUET1 tunes is that – as seen in the previous PYTHIA6 tunes –the PDFs with larger low-x gluon densities (LO∗> CTEQ6L1 > CTEQ6.6) naturally produce tunes with largerPTJIM values: this corresponds to stronger regularisation of the divergent cross-section when the gluon densitywhich drives that divergence is larger.
Plots of the most important observables used in the tuning, showing the performance of the three AUET1 tunes,may be found in Figures 4 to 9. The three AUET1 tunes are all of similar quality, and provide a significantlybetter fit to ATLAS data than the MC09 setup.
Figure 4: Comparison plots of the new HERWIG/JIMMY AUET1 (ATLAS Underlying Event Tune 1) tunes tothe ATLAS MC09 tune, against corrected ATLAS UE profile data at 7 TeV. The yellow band in the ratio plotshows the data uncertainty. 10
Figure 5: Comparison plots of the new HERWIG/JIMMY AUET1 (ATLAS Underlying Event Tune 1) tunes tothe ATLAS MC09 tune, against corrected ATLAS UE profile data at 900 GeV. The yellow band in the ratioplot shows the data uncertainty. 11
Figure 6: Comparison plots of the new HERWIG/JIMMY AUET1 (ATLAS Underlying Event Tune 1) tunes tothe ATLAS MC09 tune, against corrected ATLAS 〈pT〉 vs. Nch (transverse region) data at 900 GeV and 7 TeV.The yellow band in the ratio plot shows the data uncertainty.
Figure 7: Comparison plots of the new HERWIG/JIMMY AUET1 (ATLAS Underlying Event Tune 1) tunesto the ATLAS MC09 tune, against CDF UE ∑ pT and Nch profile (transverse region) data from min bias and20 GeV jet samples at
√s = 1800 GeV. The yellow band in the ratio plot shows the data uncertainty.
Figure 8: Comparison plots of the new HERWIG/JIMMY AUET1 (ATLAS Underlying Event Tune 1) tunes tothe ATLAS MC09 tune, against corrected CDF UE data. The yellow band in the ratio plot shows the datauncertainty. 14
Swiss Cheese psum⊥ vs. Elead⊥ (removal of 3 jets) at
√s = 630 GeV
psu
m⊥
/GeV
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removed
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20 30 40 50 60 70 80
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MC/data
Figure 9: Comparison plots of the new HERWIG/JIMMY AUET1 (ATLAS Underlying Event Tune 1) tunes tothe ATLAS MC09 tune, against corrected CDF UE data. The yellow band in the ratio plot shows the datauncertainty. 15
4 Conclusions
In Table 1 we have presented the new “AUET1” set of tunes of the HERWIG/JIMMY MC event generator toQCD data from hadron colliders, particularly data from the ATLAS 7 TeV run. The AUET1 tunes give a much-improved description of ATLAS underlying event observables over the previous MC09 tune, at the slight costof a reduced quality of fit to CDF UE data. Tuning weights have been chosen carefully to maximise the qualityof the ATLAS 7 TeV data fit, with anticipation of the higher-statistics update to the ATLAS UE data, whichwas not available in time for the MC10 tuning deadline.
We have been forced by the lack of colour reconnection in the JIMMY model (as compared to e.g. PYTHIA
6) to choose whether we consider an accurate description of pT flows or of charged particle multiplicity flowsto be important: we have chosen the former, as it is more important from a physics analysis perspective. Infuture ATLAS tuning of HERWIG/JIMMY, LEP data will be used in an earlier stage to tune the hadronisationparameters and we will attempt to incorporate additional parameters relating to beam remnant fragmentation:it is possible, although as-yet undemonstrated, that these beam remnant changes will improve upon the currentdescription of pT vs. Nch.
Additionally, on the recommendation of the authors, AUET1 uses a more sophisticated HERWIG setting forinitial state radiation than that in MC08/MC09, and we now give primordial transverse momentum to thepartons, rectifying a previous tuning oversight. The latter has visible impact on the simulation of the vectorboson pT peak, since the overpopulated zero-pT bin from MC08/09 is now smeared out to augment the pT peakat ∼ 2 GeV.
These tunes are now in use as the main HERWIG/JIMMY configurations for the ATLAS MC10 production.
16
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